Problem: Simplify the following expression: $ z = -1 + \dfrac{1}{9x - 1} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9x - 1}{9x - 1}$ $ \dfrac{-1}{1} \times \dfrac{9x - 1}{9x - 1} = \dfrac{-9x + 1}{9x - 1} $ Therefore $ z = \dfrac{-9x + 1}{9x - 1} + \dfrac{1}{9x - 1} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{-9x + 1 + 1}{9x - 1} $ $z = \dfrac{-9x + 2}{9x - 1}$